The metro is brilliant for the city centre, but once you want to head out to places like Tsaritsyno or any of the parks on the outskirts, having your own wheels suddenly makes a ton of sense. Just keep in mind that the traffic inside the Garden Ring during rush hour is absolutely brutal, so plan your pick-up and drop-off times around that. Finding a rental car around Moscow is pretty easy, you can see what is available here
https://getrentacar.com/en-US/russia/moscow .